Problem: Compute $7\left(\frac{1}{5}\right)^3$.
Solution: Recall that $\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$. Therefore  $$7\left(\frac{1}{5}\right)^3=7\left(\frac{1^3}{5^3}\right)=7\left(\frac{1}{125}\right)=\boxed{\frac{7}{125}}.$$